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Data publicarii: 16 Octombrie, 2008

IDENTITATI TRIGONOMETRICE-teorie

1)\; {\sin ^2}{a}+{\cos^2}{a}=1,\forall{a}\in{\mathbb{R}}.1)\; {\sin ^2}{a}+{\cos^2}{a}=1,\forall{a}\in{\mathbb{R}}.

2)\;\sin(-x)=-\sin{x} ,\forall{x}\in{\mathbb{R}}.2)\;\sin(-x)=-\sin{x} ,\forall{x}\in{\mathbb{R}}.

3)\;\cos{(-x)}=\cos{x} ,\forall{x}\in{\mathbb{R}}.3)\;\cos{(-x)}=\cos{x} ,\forall{x}\in{\mathbb{R}}.

4)\;{tgx} = \frac{\sin{x}}{\cos{x}},\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix} (2k+1)\frac{\pi}{2}|k\in{\mathbb{Z}}\end{Bmatrix}}.4)\;{tgx} = \frac{\sin{x}}{\cos{x}},\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix} (2k+1)\frac{\pi}{2}|k\in{\mathbb{Z}}\end{Bmatrix}}.

5)\;{ctgx} = \frac{\cos{x}}{\sin{x}},\forall{x}\in{\mathbb{R}}\setminus\{{k\pi}|k\in{\mathbb{Z}}\}.5)\;{ctgx} = \frac{\cos{x}}{\sin{x}},\forall{x}\in{\mathbb{R}}\setminus\{{k\pi}|k\in{\mathbb{Z}}\}.

6)\;{tg(-x)} = {- tgx}, \forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}(2k+1)\frac{\pi}{2}|k\in{\mathbb{Z}}\end{Bmatrix}}.6)\;{tg(-x)} = {- tgx}, \forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}(2k+1)\frac{\pi}{2}|k\in{\mathbb{Z}}\end{Bmatrix}}.

7)\;{ctg(-x)}={- ctgx},\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}k\pi|k\in{\mathbb{Z}}\end{Bmatrix}}.7)\;{ctg(-x)}={- ctgx},\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}k\pi|k\in{\mathbb{Z}}\end{Bmatrix}}.

8)\;{secx}=\frac{1}{cosx},\;\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}(2k+1)\frac{\pi}{2}|k\in{\mathbb{Z}}\end{Bmatrix}}.8)\;{secx}=\frac{1}{cosx},\;\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}(2k+1)\frac{\pi}{2}|k\in{\mathbb{Z}}\end{Bmatrix}}.

9)\;{cosecx}=\frac{1}{sinx},\;\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}k\pi|k\in{\mathbb{Z}}\end{Bmatrix}}.9)\;{cosecx}=\frac{1}{sinx},\;\forall{x}\in{\mathbb{R}}\setminus{\begin{Bmatrix}k\pi|k\in{\mathbb{Z}}\end{Bmatrix}}.  

10)\;\cos{(a+b)}=\cos{a}\cos{b}-\sin{a}\sin{b}, \forall{a,b}\in{\mathbb{R}}.10)\;\cos{(a+b)}=\cos{a}\cos{b}-\sin{a}\sin{b}, \forall{a,b}\in{\mathbb{R}}.

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